THE "THIN WIRE" PROGRAM
for Moment Method Antenna Analysis
R. P. Haviland
Daytona Beach


Abstract

Describes the capability and limitations of the antenna analysis
program developed by Richmond of Ohio State for NASA. Shows the basic
assumptions of the program, and its structure. Describes a supplementary
program to prepare data input. Includes a sample problem, with
problem parameters, data input and results output. Recommends the
program as a check for other analysis programs, and for problems not
allowed by the common MiniNEC, specifically, effect of insulation on
wires, scatter patterns and echoing area.

FORWARD

	In the early 1970's, J.H.Richmond of Ohio State University completed an
antenna analysis program under a NASA contract. While this work influenced
later activity in the field, the program itself has been largely
neglected. The purpose of this paper is to invite attention to some of the
useful concepts in the program and the theory behind it, and to show
some of the type of results it produces.

BASIC ELEMENTS OF THE THINİWIRE PROGRAM

	The heart of the program is the "reaction concept" of V.H. Rumsey
(1). This is based on the idea that any real-world measurement of the
electromagnetic field must include introduction of a probe into the
field. What is measured is not the field, but rather the reaction of the
field on the probe. The alternate term for reaction is coupling: the
author finds this easier to visualize.

	For the Thin Wire program (2,3), the field is assumed to be that
produced by current on the surface of a wire of constant diameter and
stated conductivity. Errors are present if the wire diameter is
large, with appreciable circumferential current.  The
observation point is assumed to lie on the axis of the wire for the self
reaction, or on the axis of an adjacent wire for mutual reaction.
Diameters and lengths may be independent for the two wires, but
errors will be introduced if segment lengths are greatly different.

	To simplify computation, the currents are assumed to be
sinusoidal in form. The specific relation used is of the form:

	P1*(sinh(G*(Z-Z1))/sinh(G*D1)+P2*(sinh(G*(Z3-Z))/sinh(G*D2)

where Z is position along the wire from segment end Z1 to End Z3, and
P1,P2 are switches which cause the second term to be zero for Z1<Z<Z2,
and the first term to be zero for Z2<Z<Z3. G is the complex
propagation constant, G=s(Mu*Epsilon)^1/2. D1 and D2 are 
the lengths from Z1 to Z2 and from Z2 to Z3.

	If the lengths D1 and D2 are each a quarter wavelength, the
relation is for a sinusoidal distribution along the entire
segment. Since the current on thin real wires is nearly but not exactly
sinusoidal, use of segments as long as a half-wavelength will lead to
analysis errors, essentially of the same order as for the values
developed by Carter (4) for half-wave dipoles. Segment lengths of the
order of 0.25-0.3 wavelengths will lead to relatively small errors, of
the magnitude of "two term" analyses of King (4). Note that very short
segments will lead to a triangular current distribution. These factors
may be contrasted to the assumptions for MiniNEC, a constant pulse over
the segment (except for a zero half pulse for end segments) or for NEC,
of the form, constant + sine + cosine terms.

	As usual with this type of antenna and field analysis, the formulation
leads to an impedance value:

		Em = In * Zmn

where the Zs are the self and mutual impedances of the segments, E is the
voltage impressed at one or more segments, and I are the segment
currents. Since reciprocity is assumed, the voltages may be the
response to an incident electromagnetic field. Thus
scattering and echo area problems may be handled by the same formulation.
For simplicity, impressed voltages are based on the delta gap model,
zero feed gap width with gap capacitance neglected.

	Additionally, the impedance matrix may be modified to the form:

		Zmm = Zmn + Z'mn + Z''mn

where Z' represents loading elements introduced into the array of
segments. Usually these are lumped loads, so only the elements for m=n
exist. The effect of conductor resistance is handled as a lumped
load. Z'' is a matrix representing the effect of insulation surrounding
the particular segment. Again for simplicity, approximations limit the
thickness of insulation to a few wire diameters for accurate calculation.
The current version of the program requires the insulation to be the same
thickness on all segments of the antenna, but this limitation is easily
removed, as is the current limitation of identical wire for all segments.

	The environment around the antenna may be free space, or a
medium of arbitrary dielectric constant and loss factor, for
example, sea water. However, there is no provision for an interface
between two environments, so a buried antenna must be well buried.
The original program has no provisions for the presence of
earth, but the ideal earth situation is easily handled by specifying an
image antenna.

	The program features resulting from the above approach is
summarized in Fig.1. Many of these are the identical to those of the
more common programs mentioned above. A major difference is the
availability of the insulated wire routine (although this is included
in NEC3, still of restricted availability). The external
excitation routines are available in NEC, but not in MiniNEC.

	Limitations on problems imposed by the program are summarized in
Fig.2. These are not much different than for the commonly used programs.
The use of sinusoidal current distribution does mean that somewhat
longer segments can be used than in MiniNEC, without serious loss in
accuracy. However, testing for convergence is recommended for each
new antenna configuration, by increasing the number of segments. 

	Adler (5) has extended the program to include reflection
coefficient approximation to a real earth. As in MiniNEC, his version uses
ideal earth directly under the antenna, i.e., the image technique.
However, his version does not allow the multiple ground zones of MiniNEC
or NEC.

PROGRAM INPUT AND OUTPUT

	The original Thin Wire program was written in the Fortran of the early
1970s. Input was by punched cards, and output was to a line printer.
Output was bare, a table of numbers only.

	The author has retained the same input form for data, making use of
the free form input and output features added to Fortran. This
"Input Card Deck" is created by a separate BASIC program. This requests
necessary inputs, translates these to card form, and writes the results to
a disk file, to be called by the Fortran Program. A sample input file
is shown in Fig. 3. The corresponding header output is shown in Fig. 4.
Comparison of the two clarifies the meaning of each item in the input
file. Note the use of flags to specify the type of analysis and to
control its output.

	For output, the author has added explanatory statements to the
original Fortran code. The same technique was used by Adler. The
original form is simply too abbreviated and condensed to be
useful.

	An example of output when current listing is specified is shown in Fig.
5. Both per-unit and absolute current is shown, the first as magnitude and
angle, the second as real and imaginary components. Both are shown
for each segment end. The efficiency, power and drive point impedance shown
in this figure are always output, even though current output is not
specified. The near field values are calculated and output only if
specified. A program loop may be added to the main program if near-field
values are needed at a number of points. Such calculations are expected to 
become more important, as restrictions on field intensity for health
reasons occur.

	Output with far-field calculations specified is shown in
Fig.6. There is complete freedom in specifying calculation angles. For
each one, the horizontal and vertical field components are shown,
and the total field intensity. Values may be saved for use in a
separate plot program. Adler outputsreal and imaginary field components,
and provides a plot program.

	Output with the two types of scatter calculation are shown in
Fig. 7. Cross sections and scattered field intensities are shown as
appropriate for backİscattering or biİstatic scattering. Note that the
induced current in the antenna may also be output by specifying current
print with external excitation. 

	Since the impedance matrix is calculated, its values may be output
to give the self and mutual impedances of the various segments.
Fig 8 shows such an output table for a dipole with four segments. Since
the matrix is stored in half-diagonal form to save memory, the
first four lines in the table are the values for Z11 to Z14, the next
three are for Z22 to Z24 and so on. For simplicity in use, this option
was written as a separate version of the Thin Wire program.

	The same technique can be used with the more common antenna
analysis programs. However, in the case of MiniNEC, note that the
internal matrix must be multiplied by a quantity jM before values are
output.

EXAMPLES OF PROGRAM CAPABILITY
        Since much of the Thin Wire program capability is the same as for
other programs, only two features are reviewed here.

	Fig. 9 shows the effect of adding insulation around a dipole (6). As is
easily visualized from the concepts of antenna inductance and
capacitance, adding a dielectric at the wire surface will reduce the
resonant frequency, of the order of the original frequency divided by the
square root of the insulation dielectric constant for infinitely
thick insulation. At the same time, the radiation resistance will
decrease, by the same order. These effects are very evident in the data
here. Further runs are necessary to show the other effect of dielectric
coatings, reduction in the SWR bandwidth of the antenna.

	The magnitude of change with thin coatings is often less than that
produced by other factors, such as presence of the earth, or objects in
the near field. However, the performance of antennas such as the
Yagi are very sensitive to changes in the parasitic elements, so use of the
Thin Wire analysis can save test and adjustment time.

	Fig. 10 shows the self impedance of a two-segment dipole as a function
of segment length and angle between segments. This is the "Inverted Vee"
antenna problem. The same table can be developed with the other common
analysis program, but the accuracy with MiniNEC will be poor. This table
can be extended further, with some loss in accuracy due departure from
sinusoidal current distribution in real-world antennas. Results with NEC
should be somewhat more accurate.

	In view of the known difference between MiniNEC and NEC for some
types of antennas, an important factor is comparison of outputs. Fig
11 shows the results of such a comparison, for an array of two
identical square loops fed at a corner, the diamond version of the
"quad" antenna. The thin wire and NEC results agree to about 0.4
percent in frequency for the condition of zero reactance, whereas
the MiniNEC results differ from both by some 5 percent. Complete
crossİcomparison remains to be done.

OBTAINING THE PROGRAMS

	The original thin wire program is available as a paper copy in
Fortran as 
NTIS document N74-28708,
National Technical Information
Service, Springfield, VA,22151.
The accompanying report is available as NASA CR-2396, available in
depository libraries. The Adler version is from The Naval Postgraduate School
Library, Code 0212, Monterrey, CA 93940 (the NTIS number is not known).

SUMMARY

	Experience with the Thin Wire program so far shows that its main
value is in the capability that other available programs do no have.
The most important is the insulated wire condition. The program is also
useful as a check of the results of the more common MiniNEC.

	It is a fast program, and is relatively easy to use. It  seems to
have sufficient accuracy for general use, but more checks against antenna
measurements and comparisons with other programs is needed before this
could be recommended as general practice.

REFERENCES
(1) Reaction Concept in Electromagnetic Theory, V. H. Rumsey,
Phys. Rev., n6, v94. Also in Computational Electromagnetics, IEEE
Press, NY.

(2) Computer Program for Thin-Wire Structures in a Homogeneous
Conducting Medium, J. H. Richmond, Ohio State University, Columbus,
Ohio, 1974.

(3) Radiation and Scattering by Thin-Wire Structures in the Complex
Frequency Domain, J. H. Richmond, Ohio State University, Columbus,
Ohio. A Summary is in Computational Electromagnetics, IEEE Press, NY.

(4) See the development in John D. Kraus, Antennas, 2nd ed,
McGrawİHill, NY, 1988.

(5) "ASAP" Antennas-Scatters Analysis Program: a UserİOriented Thin Wire
Antenna Computer Code, Richard W. Adler, Naval Postgraduate School
Report NPSİ62AB770801, Monterrey, CA

(6) R. P. Haviland, Insulated Antennas, Communications Quarterly,
v3, n1, Winter 1993